Such a conveying device is known from WO 2006/087088. The known conveying device is part of a transport system for container handling machines, particularly for bottle fillers. The transport system contains drivable inlet and outlet stars positioned on columnar support housings. The support housings are given a substantially tubular shape and accommodate, for instance, the drive motor for the conveying device together with its housing. The drive motor must be correctly adjusted at its predetermined place inside the outer support housing.